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Calogero-Moser Systems and Representation Theory

Author : Pavel Etingof,Pavel I. Etingof
Publisher : European Mathematical Society
Release : 2007
Category : Mathematics
ISBN : 3037190345

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Book Calogero-Moser Systems and Representation Theory Description/Summary:

Calogero-Moser systems, which were originally discovered by specialists in integrable systems, are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians. More specifically, these systems and their generalizations turned out to have intrinsic connections with such fields as algebraic geometry (Hilbert schemes of surfaces), representation theory (double affine Hecke algebras, Lie groups, quantum groups), deformation theory (symplectic reflection algebras), homological algebra (Koszul algebras), Poisson geometry, etc. The goal of the present lecture notes is to give an introduction to the theory of Calogero-Moser systems, highlighting their interplay with these fields. Since these lectures are designed for non-experts, the author gives short introductions to each of the subjects involved and provides a number of exercises.

Trends in Representation Theory of Algebras and Related Topics

Author : Andrzej Skowroński
Publisher : European Mathematical Society
Release : 2008
Category : Mathematics
ISBN : 3037190620

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Book Trends in Representation Theory of Algebras and Related Topics Description/Summary:

This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.

Calogero—Moser— Sutherland Models

Author : Jan F. van Diejen,Luc Vinet
Publisher : Springer Science & Business Media
Release : 2012-12-06
Category : Science
ISBN : 9781461212065

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Book Calogero—Moser— Sutherland Models Description/Summary:

In the 1970s F. Calogero and D. Sutherland discovered that for certain potentials in one-dimensional systems, but for any number of particles, the Schrödinger eigenvalue problem is exactly solvable. Until then, there was only one known nontrivial example of an exactly solvable quantum multi-particle problem. J. Moser subsequently showed that the classical counterparts to these models is also amenable to an exact analytical approach. The last decade has witnessed a true explosion of activities involving Calogero-Moser-Sutherland models, and these now play a role in research areas ranging from theoretical physics (such as soliton theory, quantum field theory, string theory, solvable models of statistical mechanics, condensed matter physics, and quantum chaos) to pure mathematics (such as representation theory, harmonic analysis, theory of special functions, combinatorics of symmetric functions, dynamical systems, random matrix theory, and complex geometry). The aim of this volume is to provide an overview of the many branches into which research on CMS systems has diversified in recent years. The contributions are by leading researchers from various disciplines in whose work CMS systems appear, either as the topic of investigation itself or as a tool for further applications.

Symmetry: Representation Theory and Its Applications

Author : Roger Howe,Markus Hunziker,Jeb F. Willenbring
Publisher : Springer
Release : 2015-01-04
Category : Mathematics
ISBN : 9781493915903

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Book Symmetry: Representation Theory and Its Applications Description/Summary:

Nolan Wallach's mathematical research is remarkable in both its breadth and depth. His contributions to many fields include representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. The touchstone and unifying thread running through all his work is the idea of symmetry. This volume is a collection of invited articles that pay tribute to Wallach's ideas, and show symmetry at work in a large variety of areas. The articles, predominantly expository, are written by distinguished mathematicians and contain sufficient preliminary material to reach the widest possible audiences. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors: D. Barbasch, K. Baur, O. Bucicovschi, B. Casselman, D. Ciubotaru, M. Colarusso, P. Delorme, T. Enright, W.T. Gan, A Garsia, G. Gour, B. Gross, J. Haglund, G. Han, P. Harris, J. Hong, R. Howe, M. Hunziker, B. Kostant, H. Kraft, D. Meyer, R. Miatello, L. Ni, G. Schwarz, L. Small, D. Vogan, N. Wallach, J. Wolf, G. Xin, O. Yacobi.

Xvith International Congress on Mathematical Physics (with Dvd-rom)

Author : Pavel Exner
Publisher : World Scientific
Release : 2010
Category : Science
ISBN : 9789814304634

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Book Xvith International Congress on Mathematical Physics (with Dvd-rom) Description/Summary:

The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program. This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others.

Encyclopaedia of Mathematics

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512886

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Book Encyclopaedia of Mathematics Description/Summary:

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.

Proceedings of the Workshop on Nonlinearity, Integrability and All That--Twenty Years After NEEDS '79

Author : M. Boiti
Publisher : World Scientific
Release : 2000
Category : Science
ISBN : 981024147X

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Book Proceedings of the Workshop on Nonlinearity, Integrability and All That--Twenty Years After NEEDS '79 Description/Summary:

This book discusses achievements in the last 20 years, recent developments and future perspectives in nonlinear science. Both continuous and discrete systems ? classical and quantum ? are considered.

The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems

Author : Pavel I. Etingof,Frederic Latour
Publisher : Oxford University Press on Demand
Release : 2005
Category : Mathematics
ISBN : 9780198530688

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Book The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems Description/Summary:

The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. The book, which contains many detailed proofs and explicit calculations, will be accessible to graduate students of mathematics, who are familiar with the basics of representation theory of semisimple Lie algebras.

Nonlinearity, Integrability and All That

Author : M Boiti,L Martina,F Pempinelli,B Prinari,G Soliani
Publisher : World Scientific
Release : 2000-05-12
Category : Science
ISBN : 9789814493932

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Book Nonlinearity, Integrability and All That Description/Summary:

This book discusses achievements in the last 20 years, recent developments and future perspectives in nonlinear science. Both continuous and discrete systems — classical and quantum — are considered. Contents:Advances in Analytical Methods:Nevanlinna Theory and Difference Equations of Painlevé Type (M J Ablowitz & R Halburd)Monodromy Transform Approach to Solution of Some Field Equations in General Relativity and String Theory (G A Alekseev)Nonlinear Sigma Model on Curved Surfaces: Energy and Anholonomy (R Balakrishnan)Advances in Symmetry Properties, Hamiltonian and Group Theoretical Methods:Möbius Symmetry, KP Symmetry Constraints and Calogero-Moser System (L V Bogdanov & B G Konopelchenko)KP, Modified KP, Discrete KP, Constrained KP, and q-KP (L A Dickey)On Lie Group Classification of Second-Order Ordinary Difference Equations (V Dorodnitsyn et al.)Near Integrable Systems and Perturbative Methods:Oscillatory Instability and Supercritical Dynamics of Damped-Driven Nonlinear Schrödinger Solitons (N V Alexeeva et al.)On the Existence of Radial Sine-Gordon Breathers (G L Alfimov et al.)Role of High Harmonics in Gap Soliton Evolution (G Alfimov & V V Konotop)Applications in Science and Technology:Coupled Modified Kadomtsev-Petviashvili Equations in a Higher Order Gradient Elastic Medium (C Babaoglu & S Erbay)Nonlinear Dynamics in Hydrogen Bonded Molecules (M Barthès et al.)The Window Josephson Junction: A Coupled Linear-Nonlinear System (A Benabdallah & J G Caputo)and other papers Readership: Physicists and mathematicians. Keywords:Continuous and Discrete Systems;Classical and Quantum;Nevanlinna Theory;Nonlinear Sigma Model;Mobius Symmetry;Oscillatory Instability;Supercritical Dynamics;Gap Soliton Evolution;Kadomtsev-Petviashvili Equations;Hydrogen Bonded Molecules

Mathematical Aspects of Quantization

Author : Sam Evens
Publisher : American Mathematical Soc.
Release : 2012
Category : Mathematics
ISBN : 9780821875735

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Book Mathematical Aspects of Quantization Description/Summary:

This book is a collection of expository articles from the Center of Mathematics at Notre Dame's 2011 program on quantization. Included are lecture notes from a summer school on quantization on topics such as the Cherednik algebra, geometric quantization, detailed proofs of Willwacher's results on the Kontsevich graph complex, and group-valued moment maps. This book also includes expository articles on quantization and automorphic forms, renormalization, Berezin-Toeplitz quantization in the complex setting, and the commutation of quantization with reduction, as well as an original article on derived Poisson brackets. The primary goal of this volume is to make topics in quantization more accessible to graduate students and researchers.

Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory

Author : S. Pakuliak,G. von Gehlen
Publisher : Springer Science & Business Media
Release : 2012-12-06
Category : Science
ISBN : 9789401006705

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Book Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory Description/Summary:

Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

Noncommutative Algebraic Geometry

Author : Gwyn Bellamy,Daniel Rogalski,Travis Schedler,J. Toby Stafford,Michael Wemyss
Publisher : Cambridge University Press
Release : 2016-05-20
Category : Mathematics
ISBN : 9781107129542

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Book Noncommutative Algebraic Geometry Description/Summary:

This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.

Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures

Author : Bhatia Rajendra,Pal Arup,Rangarajan G
Publisher : World Scientific
Release : 2011-06-06
Category : Mathematics
ISBN : 9789814462938

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Book Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures Description/Summary:

ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Theoretical Physics at the End of the Twentieth Century

Author : Yvan Saint-Aubin,Luc Vinet
Publisher : Springer Science & Business Media
Release : 2013-03-14
Category : Science
ISBN : 9781475736717

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Book Theoretical Physics at the End of the Twentieth Century Description/Summary:

Based on courses given at the CRM Banff summer school in 1999, this volume provides a snapshot of topics engaging theoretical physicists at the end of the twentieth century and the beginning of the twenty-first. Young physicists will find in these chapters pedagogical introductions to subjects currently active in theoretical physics, and more seasoned physicists will find a chance to share the excitement of fields outside their immediate research interests.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Author : Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Publisher : World Scientific
Release : 2019-02-27
Category : Mathematics
ISBN : 9789813272897

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Book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) Description/Summary:

The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Algebraic Geometry: Salt Lake City 2015 (Part 1)

Author : Tommaso de Fernex,Brendan Hassett,Mircea Mustaţă,Martin Olsson,Mihnea Popa,Richard Thomas
Publisher : American Mathematical Soc.
Release : 2018-06-01
Category : Geometry, Algebraic
ISBN : 9781470435776

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Book Algebraic Geometry: Salt Lake City 2015 (Part 1) Description/Summary:

This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.

Fukaya Categories and Picard-Lefschetz Theory

Author : Paul Seidel
Publisher : European Mathematical Society
Release : 2008
Category : Mathematics
ISBN : 3037190639

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Book Fukaya Categories and Picard-Lefschetz Theory Description/Summary:

The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry.

Principal Bundles

Author : Stephen Bruce Sontz
Publisher : Springer
Release : 2015-04-20
Category : Science
ISBN : 9783319158297

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Book Principal Bundles Description/Summary:

This introductory text is the first book about quantum principal bundles and their quantum connections which are natural generalizations to non-commutative geometry of principal bundles and their connections in differential geometry. To make for a more self-contained book there is also much background material on Hopf algebras, (covariant) differential calculi, braid groups and compatible conjugation operations. The approach is slow paced and intuitive in order to provide researchers and students in both mathematics and physics ready access to the material.